98 
ME. A. CAYLEY OX THE EQUATION OE DIFPEEEXCES 
the different powers of e, and write L=Mo+Mie-j-^l 2 f'+ &c.. V'=V"4-2(?B^ where 
V"=5«di+4^d^4-3cB^. We have then 
VL= V"YIo4- e I V"M,+ V"M,+ &c., 
-\-2dM, i +4cnM, +6fZM3, 
or, what is the same thing, 
iVL= V"M,+ e I V"M,+ - •• 
-j~ 4rZ]M2 I “h 4<ZM3 ,■ 
and as an equation which should be satisfied identically, and which would therefore serve 
as a verification, 
V"Mo+2fZM. = 0; 
but as a verification was obtained by other means, the equations of this kind were not 
used for the purpose. It may be interesting to give the actual calculation of one 
of the coefficients, say of coefficient 6^ (which, with coefficient 0. was calculated by 
Mr. Hakley). 
